Elaine and Paul Talbert arose at first light on Saturday, hoping the day might finally produce the breakthrough that reunites them with their missing daughter Belinda Burcham.

Last night, detectives gave the family the news they'd hoped for – Belinda was found alive.

Mr Talbert confirmed to The Sun-Herald on Saturday night that detectives had located his daughter safe and well, just a short distance away from her Double Bay home.

Belinda Burcham.

"I literally got the call just now. She was located by police on the street," he said.

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"She's now back at St Vincent's Hospital. The details are very sketchy. We don't know where she's been, how she's coped, but the important thing is that she is alive and coming home."

During the past 48 hours, the couple had donned sandwich boards carrying Belinda's image and, in the blistering heat, searched Bondi Beach and Darlinghurst for someone, anyone, who might hold the key to her whereabouts. They had planned to resume their quest on Sunday outside St Vincent's – exactly seven days since she was last seen alive.

"By trying to retrace her footsteps a week on, we might run into someone who saw her," Mr Talbert said before his daughter was found. "You have to understand, we won't rest until we find her."

Over the past week, NSW Police mounted a city-wide search for the 40-year-old mother of two, while thousands of people have viewed a Facebook page launched by her sister Justine.

On Saturday, Mrs Talbert acknowledged her daughter had been under "great strain" since separating from her partner two years ago. "There is no point in pretending that there hasn't been a very serious court battle," Mrs Talbert said. "The long and short of it is, it's left her with a broken spirit and she hasn't bounced back as quickly as perhaps other people can."

"Having said that, this is still completely out of character. For Belinda to be out of contact for almost a week has simply never happened, neither as a teenager or an adult."

Speaking candidly for the first time about events leading up to Belinda's disappearance, Mrs Talbert said alcohol-related "problems" had arisen the day before, resulting in a failed attempt to bring her back to the family house.

"It was a struggle," Mrs Talbert said. "We got Belinda into the car but, unfortunately, by the time we got to Double Bay, she asked for the window to be opened and then tried to get away."

Mrs Talbert said that due to the emotionally distressing scenes that followed, some witnesses mistakenly assumed Belinda was being abducted and called police. She later fled through a supermarket and was out of contact until 3am Sunday morning when, according to her ex-partner, she resurfaced in his back yard.

After being taken to St Vincent's Hospital, Belinda discharged herself at approximately 7.30am with CCTV footage capturing her walking out of the front doors.

A hospital spokesman confirmed Belinda still had a cannula in her arm when she departed without medical clearance. He added that while it is "not particularly uncommon" for general patients to discharge themselves, the case soon became unusual because she vanished.

Mrs Talbert said: "She's no doubt woken up in hospital and thought, 'I'm out of here'. The CCTV shows a very normal-looking person walking out with some purpose, as though she knows where she's going. The question remains where?"

Kings Cross acting commander Paul McDonald confirmed social media had generated a lot of leads that police were analysing daily.

"At this stage, we're keeping an open mind," he said before Belinda was found. "She has never gone this long without having contact with her children and we'll keep doing everything we can to locate her."

Mrs Talbert said loved ones had been clinging to the hope that she was "taking time out somewhere". However, her vast network of friends had tracked down every known acquaintance and "come up with nothing".

Fighting back tears, Mrs Talbert said: "We haven't seen the children since [Belinda disappeared], not because we don't want to, but because right now, we don't know what to say."